1. Field of the Invention
This invention relates to signal coding for pulse code modulation systems and, more particularly, to coder and decoders for telephone communication systems using compressed pulse code modulation with logarithmic companding.
2. Description of the Prior Art
The demand for communication services has been steadily increasing. In meeting this demand, it has proven effective in some communication systems to convert signals presented to the system into encoded digital signals and then reconvert the encoded digital signals into signals corresponding to those originally entered into the system. One example of a communication system in which such transmission of encoded digital signals has proven to have particular utility is a telephone communication system. Several schemes for digitally encoding signals in a telephone system are known. Although these encoding schemes are useful for both digital and analog signals entered into the telephone system, they have particular utility with continuous, time-varying analog signals such as voice signals.
In one encoding scheme, the amplitude of a voice analog signal is periodically sampled and each sample is converted into a digitally encoded pulse sequence or word representing the sampled analog signal. This operation is called sampling and quantizing the analog signal. If the range of analog signal amplitudes represented by each quantum level or step of the quantizing operation is uniform for all analog signal amplitudes, the encoded signal is said to be linear pulse code modulated (hereafter LPCM). Each LPCM signal word may then be decoded to form an analog signal of an amplitude substantially corresponding to the amplitude of the analog signal sample encoded into the LPCM signal word. Since the input analog signal was periodically sampled, the resulting, periodic LPCM signal words may be reconverted into a continuous analog signal substantially corresponding to the continuous input analog signal.
In the quantizing process, the exact level of the entered analog signal at the sampling instant is, as described, approximated by one of a number of discrete values or quantum levels digitally encoded as the LPCM signal. The difference between the instantaneous amplitude of the input analog signal and the quantum level actually transmitted is called quantizing error and gives rise to what is variously known as quantizing noise or quantizing distortion.
Quantizing distortion is especially objectionable and very often intolerable when the instantaneous amplitude of the input analog signal is small, but is usually of little or no significance when the instantaneous amplitude of the input analog signal is high. This is because the low amplitude of the input signals permits a relatively low level of quantizing noise to significantly degrade the ratio of signal to noise while a higher amplitude of the input signal can tolerate greater quantizing noise within an acceptable ratio of signal to noise. It is therefore desirable to have smaller quantum levels for lower amplitudes of the input signal to achieve closer correspondence between the quantum level of the encoded signal and the actual amplitude of the input analog signal at the lower amplitudes resulting in an acceptable ratio of signal to noise. Of course the size of the quantum levels for all input signal amplitudes could be decreased, but this produces an undesirable increase in the total number of quantum levels, requiring, for example, more bits to represent the signal as a digitally encoded word.
The suggested non-linear redistribution of the size of the quantizing levels is called companding, a verbal contraction of the terms compression and expanding. The purpose of companding is then to reduce the quantizing impairment of the original signal without unduly increasing the total number of quantizing levels by quantizing on a non-linear rather than a linear basis.
It is current practice with telephone systems to compand encoded analog signals on either a ".mu.-law" or an "A-Law" companding scheme as described by H. Kaneko in an article entitled "A Unified Formulation of Segment Companding Laws and Synthesis of Codecs and Digital Companders," published in The Bell System Technical Journal, September, 1970. The resulting signals are then called compressed pulse code modulated signals (hereafter CPCM) or companded pulse code modulated signals. The .mu.-law is being generally adopted in the United States. The "gross" continuous formulation for the .mu.-law is: ##EQU1## for -1 .gtoreq. x .gtoreq. 1. The variable x is the relative input amplitude and y the relative output amplitude, which, in turn, is encoded into a binary number expressing the magnitude of y on a linear basis. An additional bit, the "sign-bit," indicates the polarity of the signal sample x being encoded. Typically, the magnitude of y is expressed as a 6 or 7 digit binary number, corresponding to what is conventionally referred to as 7 or 8 bit resolution (code). Accordingly, y is approximated to one out of 64 or 128 evenly distrubuted levels (disregarding the sign). Actually, in the "standard" version of CPCM adopted in the U.S., a continuous exponential (or logarithmic) companding law is not used normally. Instead, the inverse function, x = f(y), is approximated by 8 linear chords or segments, each subdivided into 8 or 16 steps, depending upon the number of bits mentioned before (7 or 8). The segmented .mu.-law is used to avoid implementation difficulties and to facilitate digital linearization features, but the resulting circuits are still somewhat complicated. It might be added that regardless of approach, a constant of .mu. = 255 has been chosen. Separate studies show that the additional distortion caused by back-to-back operation of "continuous encoder" and "segmented decoder" or vice versa is acceptable, as such, of the order of 3% or less.
Another important feature of the compressed PCM code adopted in the United States is the fact that the binary scale which linearly represents the compressed relative signal magnitude, y, is reversed, or complemented -- i.e. at zero signal level the corresponding binary code, excluding the sign bit, consists of a series of all ones, while maximum signal level magnitude is represented by all zeros. The reason for this arrangement is the desire to minimize the probability of long series of zeros which would make synchronization more difficult in PCM transmissions systems. Hence a preferred embodiment of the instant invention will generate a complementary encoded representation of the compressed relative signal magnitude y.